Product of Simple Fractions
The applet below displays three fractions and their graphical representation with rows or columns of rectangular areas. In two black fractions, the digits of both the numerator and the denominator can be modified by clicking a little of their vertical midline. Clicking to the right of a digit will cause it to increase by 1; clicking to the left will decrease the digit by 1.
What if applet does not run? 
In the middle rectangle, the representations of the two fractions overlay and the middle red fraction is just the product of the other two. The product of two fractions is defined as follows

The applet illustrates why the product is defined this way. A simple fraction p/q which is read "p q^{th}," signifying p parts out of q. So a rectangle on the left is split into q equal parts (horizontal rectangles) of which p are colored green. The fraction on the right, if thought of as r/s, means taking r parts out of s, the latter are represented by vertical blue rectangles. Each of these rectangles can be split into q smaller ones:
Here are additional pages related to the definitions, properties of and operations on, fractions:
Fractions
 What Is Fraction?
 Operations on Fractions
 Equivalent Fractions
 Fraction Comparison: An Interactive Illustration
 Compare Fractions: Interactive Practice
 Fraction Comparison Sped up
 Counting and Equivalent Fractions
 Product of Simple Fractions
 What's a number? (Rational number in particular)
 Why 1/3 + 1/4 = 7/12?
 Fractions on a Binary Tree
 Fractions on a Binary Tree II
 Archimedes' Law of the Lever
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Copyright © 19962017 Alexander Bogomolny
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